MathDB
BMT 2021 Guts Round p14

Source:

October 7, 2022
algebranumber theory

Problem Statement

Given an integer cc, the sequence a0,a1,a2,...a_0, a_1, a_2, ... is generated using the recurrence relation a0=ca_0 = c and ai=ai−1i+2021ai−1a_i = a^i_{i-1} + 2021a_{i-1} for all i≥1i \ge 1. Given that a0=ca_0 = c, let f(c)f(c) be the smallest positive integer nn such that an−1a_n - 1 is a multiple of 4747. Compute ∑k=146f(k).\sum^{46}_{k=1} f(k).
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